Question

Which of the following factors can possibly make the observed linear correlation from a sample weaker than the true correlation in the population? Can be many answers.

1. Presence of a non-linear relationship

2. Outliers that deviate from the main cluster of data

3. Different correlations for different subgroups within the data

4. Range restriction on the predictor and/or criterion variables

5. Unreliable measures of the predictor and/or the criterion variables

6. Standardizing the scores on the predictor and/or the criterion

Answer 1

The factors that can possibly make the observed linear correlation from a sample weaker than the true correlation in the population are:

1) Different correlations for differnet subgroups within the data: If this is the case, then we may fail to capture the different correlations in the sample without the help of Clustering.

2) Unreliable measures of the predictor and/or the criterion variables : If the measurements or observations of the sample are not reliable, then we may end up with some rogue estimate of sample correlation that is of no use to us.

Outliers and Standardising do not have a significant effect on the correlation measure since the variation gets divided in the denominator.